Lecture Two

The wave-Particle Duality


The conclusion from the Planck (see (1-2) in chapter 1) , Einstein and Compton (see (1-3) and (1-4) in chapter 1) analyses was that light, which was thought to be a wave classically, could also behave like a particle at the quantum level. It was then natural to ask the question of whether this “particle wave duality” may apply to other objects that carry energy and momentum? For example, could a classical particle such as an electron behave like a wave at the quantum level? Indeed in 1923 DE Broglie postulated such a particle-wave duality and assigned the wavelength: Lembda=h/p


to any particle that has momentum p. This is consistent with the photon’s electromagnetic wave momentum (p=E/c =h?/c=h/?). But he proposed this momentum-wavelength relation to be true for the electron or other classical particles as well, even though the energy-momentum relation for these particles is quite different than the photon’s (i.e. E = p2/2m or E = (p2c2 + m2c4)1/2 ).

The uncertainty principle states that the uncertainty in the measurement of the position of a particle (?z) multiplied by the uncertainty in the measurement of its momentum along the same direction (?pz) are larger than the order of magnitude o